Advanced Dynamics Modeling, Duality and Control of Robotic Systems

321 Pages·2021·15.575 MB·English

by  Edward Y.L. Gu

Advanced Dynamics
Modeling, Duality and
Control of Robotic
Systems

Advanced Dynamics
Modeling, Duality and
Control of Robotic
Systems
Edward Y.L. Gu
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To my family Sabrina,
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Contents
Preface.......................................................................................................................xi
Author.....................................................................................................................xiii
Chapter1 Introduction.....................................................................................1
1.1 Kinematics,StaticsandDynamics.........................................1
1.2 DynamicsModelingandModelCompaction.........................2
1.3 ThePrinciple of Duality forRobotKinematics,Statics
andDynamics.........................................................................3
1.4 AdaptiveandInteractiveControlofRoboticSystems............4
1.5 TheOrganizationoftheBook................................................4
Chapter2 FundamentalPreliminaries..............................................................7
2.1 MathematicalPreparations.....................................................7
2.1.1 LieGroups,LieAlgebrasandTheirTopological
Structures...................................................................7
2.1.2 Manifolds,RiemannianMetrics,andEmbeddings..14
2.1.3 DifferentialConnectionsandGeodesicEquations..24
2.1.4 DualNumbers,DualVectorsandDualMatrices.....30
2.2 RobotKinematics:TheoriesandRepresentations................42
2.2.1 UniqueRepresentationsofPosition
andOrientation.........................................................42
2.2.2 TheRotationSpeedandAngularVelocity...............45
2.2.3 TheDenavit-Hartenberg(D-H)Convention............51
2.2.4 CartesianMotionvs.DifferentialMotion................60
2.2.5 KinematicSingularityandRedundancy..................65
2.3 RobotStaticsandApplications.............................................70
2.3.1 Twist,WrenchandStaticsofRoboticSystems.......70
2.3.2 StaticJointTorqueDistributions..............................71
2.3.3 ManipulabilityandPostureOptimization................73
Chapter3 RobotDynamicsModeling............................................................79
3.1 TheHistoryofRobotDynamicFormulations......................79
3.2 TheAssumptionofRigidBodyandRigidMotion..............80
3.2.1 TheRigidBodyandRigidMotion..........................80
3.2.2 KinematicParametersvs.DynamicParameters......84
3.3 KineticEnergy,PotentialEnergyandLagrangeEquations..85
3.3.1 DeterminationofKineticEnergy.............................85
3.3.2 PotentialEnergyDuetoGravityandOtherForms..94
vii
viii Contents
3.3.3 ConsistencybetweentheLagrangeandGeodesic
Equations..................................................................97
3.4 DynamicFormulationsforRoboticSystems........................99
3.4.1 DeterminationofCentrifugalandCoriolisTerms...99
3.4.2 Dynamics Modeling for a Variety of Robotic
Systems..................................................................103
Chapter4 AdvancedDynamicsModeling...................................................119
4.1 TheConfigurationManifoldandIsometricEmbedding.....119
4.2 HowtoFindanIsometricEmbedding................................122
4.3 ApplicationstoRobotDynamicsModeling.......................134
Chapter5 ThePrincipleofDualityinKinematicsandDynamics...............145
5.1 KinematicStructuresforStewartPlatform.........................145
5.2 KinematicAnalysisofDeltaClosedHybrid-Chain
Robots.................................................................................150
5.3 DualitybetweenOpenSerial-ChainandClosedParallel-
ChainSystems....................................................................159
5.4 Isometric Embedding Based Dynamics Modeling for
ParallelandHybrid-ChainRobots......................................164
5.4.1 TheStewartPlatform.............................................165
5.4.2 The3D3-LegHybrid-ChainRoboticSystem.......166
5.4.3 TheDeltaClosedHybrid-ChainRobot..................174
5.4.4 DynamicsModelingforLeggedRobots................179
5.4.5 ASummaryofDynamicsModeling......................184
Chapter6 NonlinearControlTheories.........................................................187
6.1 LyapunovStabilityTheoriesandControlStrategies..........187
6.1.1 TheLocalLinearizationProcedure........................197
6.1.2 IndirectMethodofSystemsStabilityTest.............198
6.1.3 ATheoremforDeterminationofSystem
Instability...............................................................200
6.1.4 StabilizationofNonlinearControlSystems..........201
6.2 ControllabilityandObservability.......................................205
6.2.1 ControlLieAlgebraandControllability................206
6.2.2 ObservationSpaceandObservability....................208
6.3 Input-StateandInput-OutputState-Feedback
Linearization.......................................................................211
6.3.1 TheInput-StateLinearizationProcedure...............213
6.3.2 Input-Output Mapping, Relative Degrees and
SystemsInvertibility..............................................218
6.3.3 SystemsInvertibilityandApplications..................224
6.3.4 TheInput-OutputLinearizationProcedure............226
Contents ix
6.4 IsometricEmbeddingDynamicModelandControl...........231
6.5 LinearizableSubsystemsandInternalDynamics...............234
6.6 ControlofaMinimum-PhaseSystem.................................238
6.7 ExamplesofPartiallyLinearizableSystemswith
InternalDynamics...............................................................241
Chapter7 AdaptiveControlofRoboticSystems.........................................261
7.1 TheControlLawandAdaptationLaw...............................261
7.2 ApplicationsandSimulation/AnimationStudies................270
Chapter8 DynamicsModelingandControlofCascadedSystems.............281
8.1 DynamicInteractionsbetweenRobotandEnvironment....281
8.2 CascadedDynamicsModelswithBacksteppingControl
Recursion............................................................................284
8.2.1 ControlDesignwiththeLyapunovDirect
Method...................................................................284
8.2.2 BacksteppingRecursionsinControlDesign.........289
8.3 ModelingandInteractiveControlofRobot-Environment
Systems...............................................................................296
Index......................................................................................................................303